|Identity: Two objects are never identical. Identity is a single object, to which may be referred to with two different terms. The fact that two descriptions mean a single object may be discovered only in the course of an investigation.|
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|I, 117 ff
Contingent Identity/some authors: here the Leibniz principle fails - Cresswell: better: that is only apparent identity - E.g. the largest wooden building = the most beautiful building - right: the largest wooden necessary wooden - but not necessary identical with the most beautiful - Problem: If identical, then necessary.
Necessary identity/Cresswell: if morning star = evening star, then: (if morning star and evening star nominal): false: N (morning star x)(evening star y) (x = y) but true: (morning star x)(evening star y)N(x = y) - for x = y is true in every world under an attribution V iff V(x) = V(y), and then it is true in every possible world , if it is true in one and then N(x = y) - Cresswell later: corresponds in Hughes/Cresswell/HC: "The man next door = the major" as a natural truth: that is unnatural.
HC I 167f
Identity/Hughes/Cresswell: always necessary: (x =) always underlying, even if x appears under different descriptions. The descriptions are contingent, but not the identity of the object with itself - this also applies to non-identity: it is always necessary even if the corresponding sentence is true.
M. J. Cresswell
Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988
M. J. Cresswell
Structured Meanings Cambridge Mass. 1984